Often in cancer and other medical studies, the primary response variable is the time to the occurrence of some particular event of interest (e.g. relapse of cancer, death of the patient, etc.). This kind of data is called survival data. The aim of this proposed research is to develop and extend semi-parametric Bayesian models and methodologies for the analysis of survival data obtained from various biomedical studies. The Semi-parametric models and associated methods will be sophisticated enough to deal with survival data in presence of complex censoring mechanisms, irregular data-collection schedules and missing data. Particularly in survival analysis, semi-parametric models present a popular compromise between the too restrictive parametric and too non-informative nonparametric models. A semi-parametric model has a nonparametric part (an unknown function such as a hazard or an intensity function) as well as a parametric part involving a few parameters, such as regression coefficients for explanatory variables or parameters gauging the heterogeneity in the population. The available prior information on the nonparametric part will be summarized as a stochastic process, called a prior process. The available prior information on the parametric part will be modeled as a prior distribution. The methodology developed during this project will be useful for the analysis of the panel count data (when counts of recurrent events are recorded during clinic visits), survival data with a positive probability of cure, survival data from the prevention trials, survival data from the studies with multiple outcomes par subject and survival data from the vaccine trials. Development of models, associated data analytic tools and simulation methods, and diagnostic tools for verifying the modeling assumptions will play central roles in each specific aim. New and existing methods will be evaluated and compared using data from the published literature and from other sources.